Lieb-Schultz-Mattis Theorem and the Filling Constraint
Abstract
Following recent developments in the classification of bosonic short-range entangled phases, we examine many-body quantum systems whose ground state fractionalization obeys the Lieb-Schultz-Mattis (LSM) theorem. We generalize the topological classification of such phases by LSM anomalies (arXiv:1907.08204) to take magnetic and non-symmorphic lattice effects into account, and provide direct computations of the LSM anomaly in specific examples. We show that the anomaly-free condition coincides with established filling constraints (arXiv:1705.09298, arXiv:1505.04193), and we also derived new ones on novel crystalline quantum systems.
Cite
@article{arxiv.2104.09561,
title = {Lieb-Schultz-Mattis Theorem and the Filling Constraint},
author = {Hank Chen},
journal= {arXiv preprint arXiv:2104.09561},
year = {2021}
}
Comments
24 pages, 7 figures (v2: fixed typos and amended Proposition III.2 | v3: reformatted some equations/expressions | v4: final published version)